Problem: Rewrite as a simplified fraction. ${2.9\overline{17} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2917.1717...\\ 10x &= 29.1717...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2888}$ ${x = \dfrac{2888}{990}} $ ${x = \dfrac{1444}{495}} \text{or} {2 \dfrac{454}{495}}$